With the development of means of production and circulation of digital images, and the means of imbedding relatively invisible watermarks into digital images ostensibly to convey ownership of the image, there is now financial incentive to attack an imbedded watermark in an attempt to render it non-extractable. Pixel locations of a watermarked image are presumed to correspond to those in an unmarked original image. Generally, the watermark is imbedded by altering only the values of the pixel components of the original image, not their geometric positions. This may be accomplished employing such methods as described in U.S. Pat. No. 5,825,892 which is incorporated herein by reference in its entirety.
Some methods of attacking an imbedded watermark rely on constructing a new image that is a geometrically distorted copy of the watermarked image. This new image is herein referred to as a distorted copy. Pixels in the distorted copy are placed at subtly distorted positions relative to those in the watermarked image. Pixel component values in the distorted copy are determined by two-dimensional interpolation of component values of enclosing pixel in the watermarked image. No constraints can be placed on the types of pixel position distortion an attacker might choose to use. To those skilled in the art, however, it is obvious that excessive pixel position-distortion will cause the distorted copy to be a caricature of the watermarked image, thus diminishing or destroying its economic value. Whether a distortion is excessive is a subjective measure. For a distorted copy to be useful, it requires that linear or nonlinear distortion methods that are used by an attacker have to be used sparingly and in such a manner as to produce smoothly varying and relatively small position distortions. This is so as to be essentially unobjectionable and casually unnoticeable to untrained observers. The human visual system, as a qualitative measuring device, can be relied upon to readily detect excessive distortion. It is desirable to have a method of defense that requires little or no limits to be placed on pixel position-distortions produced by the attacking method.